Plot Cumulative Distribution Function in R

In this article, we will discuss how to plot a cumulative distribution function (CDF) in the R programming Language.

The cumulative distribution function (CDF) of a random variable evaluated at x, is the probability that x will take a value less than or equal to x. To calculate the cumulative distribution function in the R Language, we use the ecdf() function. The ecdf() function in R Language is used to compute and plot the value of the Empirical Cumulative Distribution Function of a numeric vector. The ecdf() function takes the data vector as an argument and returns the CDF data.

Syntax: ecdf( data_vector )

Parameter:

• data_vector: determines the vector that contains data for CDF calculation.

Plot cumulative distribution function in base R

To plot a CDF function in base R, we first calculate the CDF by using the ecdf() function. Then we use the plot() function to plot the CDF plot in the R Language. The plot function takes the result of the ecdf() function as an argument to plot the CDF plot.

Syntax: plot( CDF )

Parameter:

• CDF: determines the cumulative distribution function calculated using the ecdf() function.

Example 1: Cumulative distribution function in base R

Here, is an example of a basic Cumulative Distribution Function Plot in the R Language.

R

# create sample data
sample_Data = rnorm(500)

# calculate CDF
CDF <- ecdf(sample_Data )

# draw the cdf plot
plot( CDF )

Output:

Example 2: Cumulative distribution function in base R using iris dataset

R

head(iris)
plot(ecdf(iris$Petal.Length))

Output:

Plot CDF of Known Distribution

To plot the cumulative distribution function of a standard distribution in a specific known range, we use the curve() function in the R Language. The curve() function draws a curve corresponding to a function over the interval. It takes an expression as an argument that in this case will be pnorm along with the limits from and to and returns a Normal CDF Plot.

Syntax: curve( expression, from, to )

Parameters:

• expression: determines the expression function for CDF calculation.
• from: determines the lower limit of data.
• to: determines the upper limit of data.

Example:

Here, is an example of a normal CDF plot.

R

# plot normal CDF plot
curve(pnorm, from = -10, to = 10)

Output:

Plot CDF of Known Distribution using ggplot2 Package

To draw the same plot in the ggplot2 package library, we use the stat_function() function. The stat_function takes the expression function as a fun argument and converts the curve according to that expression in a basic ggplot2 plot. 

Syntax: plot + stat_function( fun )

Parameters:

• fun: determines the function for the shape of the plot.

Example:

Here, is an example of a normal CDF plot using ggplot2.

R

# load library ggplot2
library(ggplot2)

# create sample dataframe for upper and lower limit
sample_limit<- data.frame(x = c(-10, 10))

# draw CDF Plot
ggplot(sample_limit, aes(x = x)) +
                  stat_function(fun = pnorm)

Output: